Not exactly sure what exactly "ballot stuffing" is, the story or should I say conspiracy theory as there are dozens of different versions some of which contain some pretty unbelievable stuff, is the occupation commission and the "reds" in the government rigged the election (both wanted the monarchy to lose though for different reasons), One extreme one is that initial counts favoured the monarchy, then a flood of votes for the republic mysteriously appeared in the last batches that had arrived at the Ministry of the interior and upturned the result. More reliable studies did show the total number of counted votes as not consistent with the number of voters. Some of boxes of ballots that never made it to Rome were discovered and promptly destroyed without being counted but that doesn't impress me much as ministry of the interior officers I worked with, though in much more recent times, told me some of that does happen but is much more likely due to an attempt to cover up administrative mistakes by "muddying the evidence" from local election officials than to affect the final results in any way. .
Quite a number of people from that generation I talked to described the voting as heavily influenced and the results as unconvincing. the north eastern areas were not able to vote as still under military occupation though what they would have voted is anybody's guess, given a chance Sud Tirol would likely have voted to be part. of Austria, which possibly they were at the time as Hitler had annexed the area, but not that sure they would have considered the monarchy the lesser evil given just those two options.
After a republican government had been created, the king went into voluntary exile, the monarchists to this day affirm he didn't contest the result to avoid a possible civil war. for sure there were a number of violent disorders resulting in several deaths.
On a link with the main subject of this thread there is also a story that Tito's forces were ready to invade in case the monarchy had won, given the state of Italian armed forces at the time this doesn't look as far fetched as it would today, the "Yugoslav scare" continued to exist in Italy well into the sixties.